Metrics for Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, A

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze1.0ms (0.1%)

Memory

1.4MiB live, 1.4MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample743.0ms (38.6%)

Memory

22.0MiB live, 953.0MiB allocated; 268ms collecting garbage

Samples

439.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 205.0ms

ival-mult: 118.0ms (57.5% of total)

ival-div: 75.0ms (36.6% of total)

exact: 7.0ms (3.4% of total)

ival-assert: 3.0ms (1.5% of total)

adjust: 2.0ms (1% of total)

Bogosity

explain50.0ms (2.6%)

Memory

8.3MiB live, 100.6MiB allocated; 12ms collecting garbage

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`#s(literal 1 binary64)`
-	-	`(*.f64 x x)`
-	-	`(/.f64 #s(literal 1 binary64) (*.f64 x x))`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	1

Precision?

0/0

Recall?

0/0

Samples

26.0ms

512×

valid

Compiler

Compiled 29 to 16 computations (44.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-mult: 8.0ms (62.4% of total)

ival-div: 3.0ms (23.4% of total)

ival-true: 0.0ms (0% of total)

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

preprocess205.0ms (10.6%)

Memory

-4.8MiB live, 248.6MiB allocated; 45ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	30	15
2	72	15
3	114	15
4	236	15
5	1307	15
6	7105	15
0	4	5
0	6	5
1	14	5
2	34	5
3	76	5
4	182	5
5	1037	5
0	8422	5

Stop Event

1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))

Outputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))

Symmetry

(abs x)

Compiler

Compiled 5 to 4 computations (20% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify158.0ms (8.2%)

Memory

11.6MiB live, 192.9MiB allocated; 32ms collecting garbage

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
0	6	10
1	14	10
2	34	10
3	76	10
4	182	10
5	1037	10
0	8422	10

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)
x

Outputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)
x

localize77.0ms (4%)

Memory

-14.2MiB live, 28.2MiB allocated; 10ms collecting garbage

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(*.f64 x x)
accuracy	0.14453125	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Samples

73.0ms

256×

valid

Compiler

Compiled 12 to 6 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 67.0ms

ival-mult: 65.0ms (96.5% of total)

ival-div: 2.0ms (3% of total)

ival-true: 0.0ms (0% of total)

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series2.0ms (0.1%)

Memory

4.3MiB live, 4.3MiB allocated; 0ms collecting garbage

Counts

2 → 2

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)

Outputs
#s(approx (/ 1 (* x x)) #s(hole binary64 (/ 1 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	((/ 1 (* x x)) (* x x))
0.0ms	x	@	-inf	((/ 1 (* x x)) (* x x))
0.0ms	x	@	inf	((/ 1 (* x x)) (* x x))

simplify186.0ms (9.7%)

Memory

-7.2MiB live, 169.6MiB allocated; 102ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	20	18
2	43	18
3	88	18
4	259	18
5	2362	18
0	8048	18

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (/ 1 (* x x)) #s(hole binary64 (/ 1 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))

Outputs
#s(approx (/ 1 (* x x)) #s(hole binary64 (/ 1 (pow x 2))))
#s(approx (/ 1 (* x x)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* x x) (*.f64 x x))

rewrite97.0ms (5%)

Memory

15.4MiB live, 60.0MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	22	6
2	82	6
0	342	6

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

2 → 43

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)

Outputs
(*.f64 (fabs.f64 (pow.f64 x #s(literal -1 binary64))) (fabs.f64 (pow.f64 x #s(literal -1 binary64))))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(pow.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal -2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1 binary64))
(pow.f64 x #s(literal -2 binary64))
(/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64))) (neg.f64 x))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64))) x)
(/.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 x))
(/.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) x)
(/.f64 (pow.f64 x #s(literal -1 binary64)) (neg.f64 x))
(/.f64 (pow.f64 x #s(literal -1 binary64)) x)
(/.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (.f64 x x)))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(neg.f64 (pow.f64 x #s(literal -2 binary64)))
(fma.f64 (fabs.f64 (pow.f64 x #s(literal -1 binary64))) (fabs.f64 (pow.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 0 binary64) (*.f64 x x)))
(fma.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 0 binary64) (*.f64 x x)))
(exp.f64 (-.f64 #s(literal 0 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (neg.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 x) #s(literal -2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)))
(+.f64 (cosh.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))) (sinh.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))))
(+.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 #s(literal 0 binary64) (*.f64 x x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (neg.f64 x) x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64)))
(neg.f64 (*.f64 x x))
(sqrt.f64 (.f64 (.f64 x x) (*.f64 x x)))
(fabs.f64 (*.f64 x x))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))

eval4.0ms (0.2%)

Memory: 9.6MiB live, 9.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 330 to 97 computations (70.6% saved)

prune2.0ms (0.1%)

Memory

5.6MiB live, 5.6MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	44	1	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	2	46

Accuracy

100.0%

Counts

46 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(pow.f64 x #s(literal -2 binary64))
✓	99.8%	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify4.0ms (0.2%)

Memory

7.2MiB live, 7.2MiB allocated; 0ms collecting garbage

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(pow.f64 x #s(literal -2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	5
0	4	5
0	4	5

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(pow.f64 x #s(literal -2 binary64))
x
#s(literal -2 binary64)

Outputs
(pow.f64 x #s(literal -2 binary64))
x
#s(literal -2 binary64)

localize30.0ms (1.5%)

Memory

-15.1MiB live, 31.8MiB allocated; 4ms collecting garbage

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(pow.f64 x #s(literal -2 binary64))

Samples

10.0ms

256×

valid

Compiler

Compiled 7 to 5 computations (28.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-pow: 3.0ms (82.2% of total)

ival-true: 0.0ms (0% of total)

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series1.0ms (0%)

Memory

2.3MiB live, 2.3MiB allocated; 0ms collecting garbage

Counts

1 → 1

Calls

Call 1

Inputs
(pow.f64 x #s(literal -2 binary64))

Outputs
#s(approx (pow x -2) #s(hole binary64 (/ 1 (pow x 2))))

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	((pow x -2))
0.0ms	x	@	inf	((pow x -2))
0.0ms	x	@	-inf	((pow x -2))

simplify255.0ms (13.2%)

Memory

-41.8MiB live, 234.7MiB allocated; 147ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	24	9
3	56	9
4	201	9
5	2236	9
0	8845	9

Stop Event

1×	iter limit
1×	node limit

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (pow x -2) #s(hole binary64 (/ 1 (pow x 2))))

Outputs
#s(approx (pow x -2) #s(hole binary64 (/ 1 (pow x 2))))
#s(approx (pow x -2) (/.f64 #s(literal 1 binary64) (*.f64 x x)))

rewrite22.0ms (1.2%)

Memory

7.3MiB live, 53.4MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
0	4	3
1	12	3
0	39	3

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

1 → 9

Calls

Call 1

Inputs
(pow.f64 x #s(literal -2 binary64))

Outputs
(*.f64 (neg.f64 (pow.f64 x #s(literal -1 binary64))) (neg.f64 (pow.f64 x #s(literal -1 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal -1 binary64))) (fabs.f64 (pow.f64 x #s(literal -1 binary64))))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal -2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1 binary64))
(pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 2 binary64))
(pow.f64 x #s(literal -2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal -2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal -2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal -2 binary64))))

eval1.0ms (0.1%)

Memory: 4.6MiB live, 4.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 68 to 27 computations (60.3% saved)

prune1.0ms (0.1%)

Memory

5.6MiB live, 5.6MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	10	0	10
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	10	2	12

Accuracy

100.0%

Counts

12 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(pow.f64 x #s(literal -2 binary64))
✓	99.8%	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes6.0ms (0.3%)

Memory

-25.1MiB live, 19.2MiB allocated; 4ms collecting garbage

Counts

2 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(pow.f64 x #s(literal -2 binary64))

Outputs
(pow.f64 x #s(literal -2 binary64))

Calls

3 calls:

3.0ms	(*.f64 x x)
1.0ms	x
1.0ms	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Results

Accuracy	Segments	Branch
100.0%	1	`(*.f64 x x)`
100.0%	1	`(/.f64 #s(literal 1 binary64) (*.f64 x x))`
100.0%	1	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes4.0ms (0.2%)

Memory

18.3MiB live, 18.3MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))

Outputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))

Calls

3 calls:

2.0ms	x
1.0ms	(/.f64 #s(literal 1 binary64) (*.f64 x x))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.8%	1	`(*.f64 x x)`
99.8%	1	`(/.f64 #s(literal 1 binary64) (*.f64 x x))`
99.8%	1	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify48.0ms (2.5%)

Memory

18.8MiB live, 62.4MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	8	8
2	11	8
3	19	8
4	42	8
5	215	8
6	2161	8
7	5325	8

Stop Event

1×	node limit

Calls

Call 1

Inputs
(pow.f64 x #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (*.f64 x x))

Outputs
(pow.f64 x #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (*.f64 x x))

derivations2.0ms (0.1%)

Memory

7.7MiB live, 7.7MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 8 to 6 computations (25% saved)

preprocess26.0ms (1.4%)

Memory: -30.4MiB live, 67.9MiB allocated; 13ms collecting garbage
Remove: (abs x)
Compiler: Compiled 48 to 40 computations (16.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze1.0ms (0.1%)

sample743.0ms (38.6%)

explain50.0ms (2.6%)

preprocess205.0ms (10.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify158.0ms (8.2%)

localize77.0ms (4%)

series2.0ms (0.1%)

simplify186.0ms (9.7%)

rewrite97.0ms (5%)

eval4.0ms (0.2%)

prune2.0ms (0.1%)

simplify4.0ms (0.2%)

localize30.0ms (1.5%)

series1.0ms (0%)

simplify255.0ms (13.2%)

rewrite22.0ms (1.2%)

eval1.0ms (0.1%)

prune1.0ms (0.1%)

regimes6.0ms (0.3%)

regimes4.0ms (0.2%)

simplify48.0ms (2.5%)

derivations2.0ms (0.1%)

preprocess26.0ms (1.4%)

end0.0ms (0%)

Profiling